Electrical impedance tomography method and electrode arrangement for use therein

ABSTRACT

An electrode arrangement for an electrical impedance tomography system comprises a plurality of electrodes in an array mounted in a support medium for supporting the electrodes adjacent a surface of a volume the electrical conductivity distribution of which is to be measured, for example the thorax or another body part, a pipeline, the ground, and so on. The electrodes are disposed in two groups, the arrangement being such that, in use, one group will be closer to the surface than the other group, In operation, applying a known current to them. For each stimulated pair, a resulting potential difference will be recorded at the pair of the remaining electrodes which, if stimulated, would produce an electric field with vectors of the electric field produced by the stimulated pair of electrodes.

TECHNICAL FIELD

The invention relates to a method of performing electrical impedancetomography measurements and electrode arrangements for use therein.

The invention is applicable generally to the imaging of electricalimpedance variations in conductive media, and especially in volumeconductors such as parts of the human body, the ground, pipelines, andso on.

BACKGROUND ART

Electrical impedance tomography (EIT), also known as “applied potentialtomography” (APT), is used to provide images of spatial variations inelectrical impedance within a conductive volume conductor. Theelectrical impedance changes are measured by providing an array ofelectrodes about the volume to be imaged. A stimulus current is suppliedto each pair of electrodes in turn and the resulting potentialdifferences recorded between pairs of the remaining electrodes. Theprocess is repeated until all of the independent combinations ofstimulation/recording are exhausted. The measurements are used todetermine the transfer impedance changes and construct an image of thevolume. In contrast to X-ray computer tomography applications, where thepaths of photons through a body are straight lines, the current paths inEIT are functions of an unknown electrical conductivity distribution.This gives rise to a non-linear image reconstruction problem.Nevertheless, algorithms have been devised for converting the series ofmeasurements into an image of the electrical impedance distributionwithin the body at a sufficiently high rate that changes associated withrespiratory and cardiac functions, for example, can be monitored.

The quality of the image depends upon the sensitivity of the measuringsystem, which typically varies with distance from the electrodes. Inclinical applications, for example, where the electrodes are distributedaround the body part to be measured, such as the thorax, difficultiesmay be encountered in resolving impedance changes which occur deep inthe body. Most attempts to improve image quality have focused upon thereconstruction algorithms, as disclosed, for example, in U.S. Pat. Nos.4,617,939, 5,381,333 and 5,465,730. Limited attention has been devotedto the electrode arrangement. For example, a study of various electrodeconfigurations was described by Booth et al. in “A Comparison of ThreeElectrode Configurations for Electrical Impedance Tomography”, IEEColloquium on “Innovation in Instrumentation for Electrical Tomography”,pp. 11/1, 11/3, 1995. British patent application number 2,257,530disclosed electrodes in a circular array or “rosette” placed upon asubstantially flat part of the body, such as the chest. This was said tobe especially desirable when imaging the heart, since impedance changesoccurring in the heart during the cardiac cycle will be larger thanthose occurring in the region of the skin.

Little attention has been paid to the way in which the measurementsthemselves are made. There are two kinds of procedure for taking themeasurements. One involves applying stimulation currents simultaneouslyto a ring of electrodes to generate a current pattern and simultaneouslymeasuring the corresponding voltage distribution around the same oradjacent electrodes. An example of such an approach is described in anarticle by P. Hua et al. entitled “An Electrical Impedance Tomographusing Compound Electrodes”, presented at the IEEE Engineering inMedicine & Biology Society 11th. Annual International Conference, 1989.Hua et al. described experiments with thirty-two compound electrodesencircling a body to be measured. Each compound electrode comprised aninner electrode surrounded by an outer electrode with an annular spacebetween them. In some cases, Hua et al. short-circuited the inner andouter electrodes and used them for both stimulation and recording. Inother cases, Hua et al. injected a spatially-sinusoidal current patterninto the ring of 32 outer electrodes and recorded the correspondinggenerally sinusoidal voltage distribution around the ring of 32 innerelectrodes. This approach requires 32 adjustable current generatorswhich must be adjusted individually to give the required pattern asaccurately as possible, making it difficult to obtain repeatablemeasurements accurately. Also, the equipment is complex and costly.

An example of the other kind of procedure is described in U.S. Pat. No.4,617,939 (Brown et al.) issued October 1986. Brown et al. describepositioning 16 electrodes around a body, applying a current to a firstpair of the electrodes and recording the potential difference betweenevery other pair of the remaining electrodes. As also noted by Hua etal. (supra), significant contact impedance between the electrodes andthe body surface militates against measurement sensitivity, so Brown etal. avoid using the same electrode for both stimulation and recording.Brown et al. repeat the procedure, applying current to pair ofelectrodes in turn. For each pair, Brown et al. measure voltages at allof the remaining electrodes. In practice, such a procedure would not beentirely satisfactory because many of the voltage measurements would becomparable with noise levels.

The present invention seeks to mitigate the disadvantages of these knownEIT systems and provide an improved electrical impedance tomographyprocedure with enhanced sensitivity to changes in the electricalconductivity distribution inside the body of interest.

DISCLOSURE OF INVENTION

According to one aspect of the invention, a method of determiningelectrical impedance tomography of a conductive volume comprises thesteps of selecting, in turn, each of a plurality of pairs of locationsupon a surface of the conductive volume, supplying a stimulation currentto the surface by way of the selected pair of locations, and recording,for each selected pair of locations, a resulting potential differencebetween at least one pair of the remaining locations, characterized inthat, the steps of, for a particular pair of locations stimulated,selecting from among the remaining locations, for recordal, the pair orpairs of locations which, if stimulated, would produce an electric fieldwith vectors most closely aligned with the corresponding vectors of theelectric field produced by stimulation of said particular pair oflocations, and recording said potential difference at the or each saidpair of locations so selected for recordal.

The above method may be performed using a plurality of electrode means,each disposed upon or adjacent said surface at a respective one of saidplurality of locations, each electrode mean being used to applystimulation current to, or record potential at, said respective one ofsaid locations.

Each electrode means may comprise two electrodes, that are closelylocated spatially, one for stimulation and the other for recording. Oneelectrode may be disposed inside the other in a plane which, in use,will be parallel to the said surface. The stimulation current could thenbe applied to two outer electrodes and the potential difference measuredat a said selected pair comprising the corresponding two innerelectrodes. Conversely, the stimulation current could be applied to thetwo inner electrodes and the potential difference remeasured at thecorresponding outer electrodes.

Alternatively, each electrode means may comprise a first electrode and asecond electrode spaced apart from each other in a direction which, inuse, will be substantially normal to the said surface. The stimulationcurrent could be applied by way of two of said second electrodes and thepotential difference measured between two of said first electrodes, orvice versa.

According to another embodiment of the invention, a method of measuringelectrical conductivity distribution within a conductive volume includesthe steps of positioning adjacent a surface of the body an array ofelectrodes, with a first group of the electrodes closer to the surfacethan a second group of the electrodes, applying a stimulation current toselected pairs of electrodes in turn and measuring, for each pairstimulated, corresponding electrical potential differences producedbetween pairs of the remaining electrodes, and processing the measuredpotential differences to determine electrical conductivity variationswithin the body.

According to another aspect of the present invention, an electrodearrangement for an electrical impedance tomography system comprises aplurality of electrodes and support means for supporting the electrodesadjacent a surface of a conductive body the conductivity of which is tobe mapped by the system, the arrangement being such that a first groupof said plurality of electrodes will be closer to the surface than asecond group of the plurality of electrodes.

According to yet another aspect of the invention, an electrodearrangement for an electrical impedance tomography system comprises aplurality of electrodes in an array mounted in a support medium forsupporting the electrodes adjacent a surface of a volume to be imaged,the support medium having anisotropic conductivity, its conductivity ina direction that, in use, is normal to the surface, being significantlygreater than its conductivity in a transverse direction.

According to a further embodiment of the invention, an electrodearrangement for an electrical impedance tomography system comprises anarray of electrodes fixed spatially relative to each other in a rigidsupport medium, and an interface medium for interfacing the rigidsupport to a surface of a conductive volume to be measured, theinterface medium being conductive so as to connect the electrodeselectrically to the surface and pliable so as to conform to variationsin relief of the surface.

An advantage of this electrode arrangement of such further aspect, ascompared with electrodes which are simply attached directly to thevolume, is that the relative position of the electrodes, and thedimensions of the array, are fixed, which facilitates static imagereconstruction of the image.

According to yet a further aspect of the invention, an electrodearrangement for use in electrical impedance tomography comprises aplurality of electrode means each formed by a stimulation electrode anda recording electrode closely located spatially. In one embodiment ofthis aspect, the electrode means comprises an inner electrode surroundedby an outer electrode with an annular channel between them. Electricallyinsulating sealing means may be provided in the annular channel forcontacting said surface, in use, and insulating the inner electrodeelectrically from the outer electrode.

Various objects, features, aspects and advantages of the presentinvention will become more apparent from the following detaileddescription of preferred embodiments of the invention, taken inconjunction with the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1, labelled PRIOR ART, is a diagram of the generic components thatare part of a typical EIT apparatus;

FIG. 2 is a diagram of a first embodiment of the invention comprising anannular EIT electrode array;

FIG. 3 is a three-dimensional view of the annular electrode array ofFIG. 2;

FIG. 4 is a cross-sectional detail view taken on the line IV—IV of FIG.2;

FIG. 5 compares the sensitivity values of the annular EIT electrodearray of FIG. 2 with those of the EIT system of FIG. 1, for radialpositions;

FIG. 6 illustrates the sensitivity theorem used in determiningelectrical impedance tomography (EIT) of a volume conductor;

FIG. 7 is a flowchart representing a typical measurement procedure usingthe electrode means of FIG. 2;

FIG. 8 is a plan view of an alternative form of electrode means,comprising an inner electrode and an outer electrode (also referred toas a compound electrode;

FIG. 9 is a cross-sectional view of the electrode means of FIG. 8;

FIG. 10 illustrates a second embodiment of the invention in the form ofa planar rectangular electrode array for a ground probing application;

FIG. 11 illustrates one cell of the electrode array of FIG. 10;

FIG. 12 illustrates a third embodiment in the form of a cylindricalelectrode array for three-dimensional imaging of a human torso; and

FIGS. 13A to 13I illustrate the image reconstruction obtained from aconventional EIT electrode array, such as that shown in FIG. 1, and anelectrode array in which the stimulating electrodes and recordingelectrodes are co-located, such as that shown in FIG. 2.

BEST MODES FOR CARRYING OUT THE INVENTION

Referring to FIG. 1, a typical known EIT apparatus comprises anelectrode array comprising sixteen electrodes E₁ to E₁₆ distributed,equally spaced apart, around a conductive volume 12, to which they areattached directly, if necessary with a suitable conductive gel ensuringgood electrical contact. The conductive volume 12 may be, for example, ahuman thorax. The electrodes are connected by a link 14 to electronicconditioning circuitry 16 which will usually include components such asa current source controlled by a D-to-A-converter, an A-to-D converter,differential amplifier, filter, analog multiplexer, clock, and thedigital I/O required to control the circuitry from a computer 18 towhich the electronic conditioning circuitry is connected. The computer18 may be a personal computer equipped with a digital signal processorcard used for the image reconstruction process and a suitable display 20for displaying the images.

Using the procedure disclosed in U.S. Pat. No. 4,617,939, a first pairof the electrodes E₁ and E₂ are stimulated by injecting a current of,say, 4 mA at 50 kHz, into them and the corresponding potentialdifferences measured between each of the other pairs of electrodes, i.e.(E₃-E₄), (E₄-E₅), (E₅-E₆), and so on up to (E₁₅-E₁₆). The potentialdifferences between electrodes E₁₆ and E₁, E₁ and E₂, and E₂ and E₃ arenot measured because the voltage drop across the contact resistance dueto the injected current would affect the measurements.

The next pair of electrodes E₂ and E₃ then are stimulated and thepotential differences between pairs of the other electrodes measured.The procedure is repeated until all of the pairs of electrodes have beenstimulated in turn. The accumulated measurements are processed by thecomputer 18 and an image of the electrical impedance variation acrossthe conductive volume is created and displayed on display unit 20.Various algorithms have been disclosed for computing these impedancevariation, such as the so-called “back-projection” reconstructionalgorithm and the regularized inverse of the sensitivity matrix.

While this procedure might appear satisfactory theoretically, inpractice, noise may obscure many of the readings and reduce the qualityof the reconstruction. Embodiments of the present invention favour highsignal-to-noise ratio measurements by limiting the measurements, for agiven stimulation pair, to that pair or pairs whose “recording” electricfield vectors most closely align with the electric field vectors of thestimulated pair of electrodes. It will be appreciated that the recordingelectrodes measure potential difference so their “recording” electricfield vectors is really that which would be produced if a stimulationcurrent were injected into them. Generally, the present invention aimsto keep the stimulating and recording electric field vectors as close toeach other as possible. (Ideally, they would be superimposed). Variousarrangements for doing so will now be described.

A first embodiment of the invention will now be described with referenceto FIGS. 2 and 3 in which the electronic conditioning circuitry 16′,computer 18′ and display unit 20′ are similar to those of FIG. 1 and sohave the same reference numerals, but with a prime.

The electrode array 22 shown in FIGS. 2 and 3 differs from that shown inFIG. 1 in that it comprises two groups of electrodes arranged in anannular configuration, i.e. in two rings, one within the other, andsupported by an annular support. The inner group comprises recordingelectrodes R₁ to R₁₆ and the outer group comprises stimulatingelectrodes S₁ to S₁₆. The annular support comprises annular flanges 24and 26 (see FIG. 4) bonded to opposite sides of an array of radialseparators 28 ₁-28 ₁₆ and a circumferential band 30 is bonded to theirrespective outer edges, forming a ring of wedge-shaped compartments orcells 32 ₁ to 32 ₁₆ which are open at their inner ends 34 ₁ to 34 ₁₆ andalternate with separators 28 ₁ to 28 ₁₆. The annular flanges 24 and 26,separators 28, and outer band 30 are of insulating material. Each pairof an inner electrode R and an outer electrode S mounted in acorresponding one of the plurality of wedge-shaped compartments or cells32 ₁ to 32 ₁₆.

The wedge-shaped compartments 32 ₁ to 32 ₁₆ are equally distributed andeach subtends a 15 degree angle. They contain a conductive materialwhose electrical conductivity is comparable to the expected averageelectrical conductivity of the imaging medium. For example, formeasuring a human body part with a conductivity of, say, 0.002 mho/cm,the compartments 32 ₁ to 32 ₁₆ might contain agar jelly formed by mixingagar powder with saline solution to form a conductive gel, giving aconductivity for the wedge-shaped compartment of about 0.002 mho/cm. Theseparators 28 ₁ to 28 ₁₆ are poorly conductive and each subtends anangle of 7.5 degrees so that the annular support is circular. Theseparators 28 ₁ to 28 ₁₆ might be of synthetic plastics material, forexample polypropylene.

In use, a conductive interfacing medium 36, for example sponge materialsoaked in saline solution, is provided between the conductive volume orbody 12′ and the innermost surface of the annular support 22, i.e. theinnermost surface of the agar jelly filling the compartments 32 ₁ to 32₁₆. The sponge 36 is pliable and conforms to the shape of the conductivevolume surface. It connects each of the electrodes R₁ to R₁₆ and S₁ toS₁₆ electrically to the surface of conductive volume 12′. Theconductivity of the interfacing medium 36 is comparable to theconductivity of the imaging medium 12′.

The mounting of the electrodes S₁ to S₁₆ in compartments 32 ₁ to 32 ₁₆is the same in each case, so only the mounting of electrodes S₄ and R₄described—as an example. Thus, the stimulation electrode is mounted uponthe inner face of band 30 and connected through the band to terminal 38₄. The recording electrode R₄ is suspended in the middle of thecompartment 32 ₄ by a plastics ligature 40 ₄, extending from the annularflange 26 and a conductive filament 42 ₄ extending from the otherannular flange 24. The filament 42 ₄ connects to terminal 44 ₄ on theouter surface of flange 24. The terminals 38 ₁ to 38 ₁₆ and 44 ₁ to 44 ₄are not shown in FIGS. 2 and 3 for clarity.

The terminals 38 and 44 are connected to the electronic conditioningcircuit 16′. For convenience, the individual connections are not shownin FIGS. 2 and 3. The circuit 16′ permits selection of individual pairsof the outer electrodes S₁-S₁₆ for stimulation by a suitable current of,say, 0.1-1 mA at 10-100 kHz, and selection of pairs of the innerelectrodes R₁-R₁₆ for measurement of potential differences across them.Each of the electrodes R₁ to R₁₆ and S₁ to S₁₆ comprises a disc mountedwith its plane normal to a radius of the annular support, each pair ofelectrodes in a cell being aligned radially, i.e. on a line extendingnormal to the surface of the body 12′. Each electrode is about 6 mm indiameter. The electrodes R₁ to R₁₆ and S₁ to S₁₆ in their respectivecompartments are spaced apart radially by a distance sufficient toreduce/avoid shielding effects. Other sizes of electrodes, for examplefrom 2 mm to 10 mm diameter, are available. If they were used, thespacing would be adjusted appropriately.

In view of the alternating “high” conductivity of compartments 32 ₁ to32 ₁₆ and “low” conductivity of separators 28 ₁ to 28 ₁₆, the annularsupport can be considered to have anisotropic conductivity, i.e. highconductivity for currents flowing radially from an electrode S towardsthe volume 12′ and low conductivity for currents flowingcircumferentially from one compartment towards its neighbour.

The manner in which this arrangement of electrode geometry and mediafavours the enhancement of the sensitivity of the apparatus will now bedescribed.

FIG. 5 illustrates the average sensitivity, in the radial direction,obtained using a finite element model, for an electrical impedancetomography apparatus using the annular electrode array of FIG. 2, andthat for an equivalent conventional electrical impedance tomographyapparatus using the electrode array of FIG. 1. In both cases theconductive volume 12′ has a radius of 10 cm, with a uniformconductivity. For proof of concept, the annulus in FIG. 2 extends from10 cm to 15 cm and has a conductivity 10 times larger than theconductivity of conductive volume 12′. The medium separating theindividual compartments, i.e. of separators 28 ₁ to 28 ₁₂, is set to aconductivity value of 1% of the conductivity of conductivity volume 12′.

The average sensitivity curve obtained for the conventional electrodearray of FIG. 1 uses configurations of stimulator and recordingelectrode pairs as disclosed by Brown et al. in U.S. Pat. Nos. No.4,617,939. As mentioned earlier, in this approach, a pair ofneighbouring electrodes is used to stimulate while the electricalpotential is measured with the remaining pairs of electrodes. Theprocess is repeated until all the independent combinations areexhausted. The electrodes used for stimulation, however, are not usedalso for measurement.

The average sensitivity curve for the electrode configuration shown inFIG. 2 is obtained using pairs of electrodes in the outer group S₁-S₁₆to apply stimulation current and the corresponding pairs of electrode inthe inner group R₁-R₁₆ to measure the resulting electrical potential.

The resolution of the reconstructed image depends upon the sensitivityof the apparatus to changes of the electric conductivity in theconductive volume 12′. The sensitivities depicted in FIG. 5 wereobtained using the sensitivity expression described by D. B. Geselowitzin “An Application of Electrocardiographic Lead Theory to ImpedancePlethysmography”, IEEE Trans. Biomed. Eng., Vol. BME-18, pp. 38-41,January 1971, and by J. Lehr in “A Vector Derivation Useful in ImpedancePlethysmographic field calculation”, IEEE Trans. Biomed. Eng., Vol.BME-19, pp. 156-157, March 1972.

The theoretical basis for the reconstruction algorithm employed byembodiments of the invention will be described with reference to FIG. 6.When the conductivity distribution changes from σ(x,y,z) toσ(x,y,z)+Δσ(x,y,z), the change in the transfer impedance ΔZ for the pairof stimulating electrodes (A,B) and recording electrodes (C,D) can begiven as: $\begin{matrix}{{\Delta \quad Z} = {- {\int{{\Delta\sigma}{\frac{\overset{\rightarrow}{\nabla}{\varphi (\sigma)}}{I_{\varphi}} \cdot \frac{\overset{\rightarrow}{\nabla}{\psi \left( {\sigma + {\Delta\sigma}} \right)}}{I_{\psi}}}{v}}}}} & (1)\end{matrix}$

where:

Φ is the potential distribution when the current I_(Φ) is applied to theelectrode pair (A,B).

Ψ is the potential distribution when the current I_(Ψ) is applied to theelectrode pair (C,D).

σ(x,y,z) is the conductivity distribution when Ψ is established forI_(Ψ)

σ(x,y,z,)+Δσ(x,y,z) is the conductivity distribution when Ψ isestablished for I_(Ψ).

The term {right arrow over (Δ)}ψ(σ+Δσ) in expression (1) can be expandedwith respect to Δσ. Assuming small Δσ's, the higher order terms can beneglected and expression (1) is expressed as follows: $\begin{matrix}{{\Delta \quad Z} = {- {\int{{\Delta\sigma}{\frac{\overset{\rightharpoonup}{\nabla}{\varphi (\sigma)}}{I_{\Phi}} \cdot \frac{\overset{\rightharpoonup}{\nabla}{\Psi (\sigma)}}{I_{\psi}}}{v}}}}} & (2)\end{matrix}$

Since the term ΔZ, the difference between the measured transferimpedance and the assumed transfer impedance, is known, the differencein the conductivity distribution Δσ can be obtained. Dividing the regionof interest into small domains over which the conductivity is assumedconstant enables expression (2) to be discretized and expressed as thefollowing matrix equation: $\begin{matrix}{{\Delta \quad Z_{i}} = {\sum\limits_{j = l}^{m}\quad {S_{ij}{\Delta\sigma}_{j}}}} & (3)\end{matrix}$

where:

ΔZ_(i) is the difference in transfer impedance for the ith combinationof a pair of stimulating electrodes and a pair of recording electrodes;

Δσ_(j) is the unknown conductivity difference for the region element j;

S_(ij) is the sensitivity coefficient term for the stimulating/recordingelectrode pair combination i, at the element j; and

m is the number of domains into which the region has been divided.

The term S_(ij) is given as follows: $\begin{matrix}{S_{ij} = {- {\int_{v_{j}}{\left( \frac{{\overset{\rightharpoonup}{\nabla}\Phi} \cdot {\overset{\rightharpoonup}{\nabla}\Psi}}{I_{\Phi}I_{\Psi}} \right)\quad {v_{j}}}}}} & (4)\end{matrix}$

An examination of expression (4) indicates that the sensitivity term canbe enhanced by an apparatus that could maximize the integrand.Sensitivity enhancement is achieved by selecting configurations ofstimulating and recording electrode pairs that favour the scalar productin the numerator and using an annulus medium with an anisotropicconductivity that limits the current intensities at the denominator.

Electrode configurations. The annular electrode array of FIG. 2 allowselectrode configurations that can maximize scalar products ofstimulating and recording electric field vectors more so than could beobtained with the electrodes of FIG. 1. It permits more combinations ofelectrodes to be made, with a greater number of different geometries.

It should be appreciated that the stimulating electrodes need not bediametrically opposite each other. Referring to FIG. 2, using pairs ofelectrodes in the outer group S₁ to S₁₆ to stimulate the body and pairsof electrodes in the inner group R₁ to R₁₆ to measure the resultingelectrical potentials tends to maximize the scalar product in thenumerator of expression (4).

Annulus conductivity. The sensitivity of the apparatus to a change inthe electrical conductivity at a position (x,y) in the conductive volumeis an inverse function of the product of the total electric currentintensities that would be required to produce the electric fieldintensity of the stimulating and recording electrode pairs at position(x,y). Disposing the electrodes in sectors whose boundaries are poorlyconductive, produces an annulus medium with an anisotropic conductivity,vis. conductive in the radial direction and poorly conductive in thedirection. This arrangement forces the current to flow in the medium ofinterest, i.e. the conductive volume, as opposed to the extended medium.It favours a larger ratio of the electric field to current intensity, inthe medium of interest.

The sensitivity function used to determine the average sensitivitiesrepresented in FIG. 5 was not optimized for the various parameters thatdefine the annulus. Key parameters are expected to be the following:

A. Annulus dimension: The size of the annulus used for this evaluationhas an outer to inner radius ratio of 1.5. Evaluations have shown thatas the ratio increases, and the electrodes are set further away from theimaging volume, the sensitivity decreases. Conversely, as the ratiodecreases, and the electrodes get closer to the imaging medium and thesensitivity increases. Although this is true for a discrete pointelectrode model, the optimal practical ratio will be determined by thesize of the electrodes and the minimum separation required to avoidmutual shielding.

B. Annulus electrical conductivity: Enhanced sensitivity is obtainedwhen the annulus is configured with an anisotropic electricalconductivity distribution, that is, a large ratio of the radial to theazimuthal electrical conductivity. No significant improvement was gainedby decreasing the azimuthal electrical conductivity below 1% of theaverage imaging medium electric conductivity.

C. Electrodes: A minimum of 32 electrodes were considered, arranged intwo concentric rings. For this evaluation, each wedge-shaped compartmentheld two electrodes, aligned along the diameter. One electrode waspositioned at the edge of the annulus and the other was positioned atthe centre of the annulus. Although this was effective for the model, inpractice, of course, the other electrode cannot be any closer to thecentre than the inner surface of the annulus. It is expected thatstandard commercial AgCl disk shaped electrodes would be used for thisapplication.

Measurement procedure. As stated earlier, it is desirable to maximizethe scalar product of the electric field vectors for the stimulatingpair of electrodes and the “recording” electric field vectors for therecording pair of electrodes. Consequently, for a given pair ofstimulating electrodes, it is sufficient to measure the potentialdifference between that pair or pairs of electrodes which are closestspatially to the stimulating electrodes and not to measure the potentialdifferences between other pairs of electrodes. This measurementprocedure will now be described with reference to the flowchart of FIG.7. In order to illustrate the stimulation/measurement strategyexplicitly, an example will be given using the geometry depicted in FIG.2. The outer electrode set (S₁-S₁₆) are used as stimulating electrodesand the inner electrode set (R₁-R₁₆) as recording electrodes. It shouldbe appreciated that the outer set could be replaced with a set on theinner surface, as per the comments above.

Following positioning of the electrodes S₁-S₁₆ and R₁-R₁₆ upon theconductive volume to be imaged, an initial conductivity distributionappropriate to the volume would be assumed (step 7.1). In the absence ofother information from, say, previous measurements of the same orsimilar volumes, a uniform mean conductivity distribution would beassumed. For example, for landmine detection, this might be a typicalconductivity distribution of the particular type of soil whereas, forhuman body imaging, it might be a typical conductivity distribution forthat part of the human body.

In step 7.2, a series of measurements are made, passing a known currentthrough each pair of stimulation electrodes S₁ to S₁₆ in turn andrecording the potential difference across the “closest” pair ofelectrodes, i.e. having the recording electric field vectors mostclosely aligned with those of the stimulating pair of electrodes. Forexample, when stimulating S₁ and S₂, the potential difference between R₁and R₂ only would be measured.

The stimulation/recording pairings proposed here are:

TABLE 1 Stimulate/Measure Configuration Stimulation Pair Recording PairPair Gap S₁,S₂ R₁,R₂ 1 S₂,S₃ R₂,R₃ 1 S₃,S₄ R₃,R₄ 1 . . . . . . . . .S₁,S₃ R1,R₃ 2 S₂,S₄ R₂,R₄ 2 . . . . . . . . . S₁,S₄ R₁,R₄ 3 . . . . . .. . .

This pattern yields 120 independent combinations for 16 compoundelectrodes (stimulate-record pairs). It should be noted that thestimulating electrodes and the recording electrodes are alwaysidentically numbered, and hence closely located. Otherstimulation/recording electrode configurations which share this featurewill have some benefit. An example of such an alternative, possible withonly a single set of electrodes as shown in FIG. 1 (denoted E₁,E₂ . . .E₁₆) is:

TABLE 2 Alternative Stimulate/Record Configuration Stimulation PairRecording Pair Pair Gap E₁,E₃ E₂,E₄ 2 E₂,E₄ E₃,E₅ 2 E₃,E₅ E₄,E₆ 2 . . .. . . . . . E₁,E₄ E₂,E₅ 3 E₂,E₅ E₃,E₆ 3 . . . . . . . . .

This pattern has a reduced number of independent combinations, since itstarts with a stimulating electrode gap of 2, for example, but will showsome of the benefit of the proposed configuration, and is shown as asimple example of an alternative manifestation of the stimulate/recordconfiguration described herein.

Referring again to the flowchart of FIG. 7, once the measurements havebeen made, in step 7.3, the region of interest, i.e. the region in whichcurrent might flow, is divided into a mesh of elements. In FIG. 2, theregion of interest is the conductive volume 12′, the sponge 36 and theannular array of compartments 32 ₁-32 ₁₆. Each element has dimensionsequal to approximately 10 per cent of the spacing between each pair ofthe recording electrodes R₁ to R₁₆. The mesh could be triangular orrectangular, as desired, and the region could be two-dimensional orthree-dimensional.

In step 7.4, the sensitivity matrix S_(ij) is calculated for the meshusing the electrode geometry, initial conductivity distribution, andapplied currents, according to equation [4], for the region of interest.

In step 7.5, an estimate is made of the noise present in the potentialdifference measurements divided by the applied stimulation current. Thisscaled noise value is used to determine a parameter μ which is the ratioof the scaled noise value to the root mean square (RMS) of the initialconductivity distribution.

In step 7.6, the pseudo-inverse S^(#) _(ij) of the sensitivity matrixS_(ij) is calculated according to equations (5) and (6).

In step 7.7, the differential conductivity distribution Δσ is calculatedaccording to equation (7).

Preferred Electrode Configuration and Compound Electrodes.

Compound electrodes are so named because they comprise two parts, onepart being used for stimulation and the other for recording. It has beenfound that compound electrodes, in conjunction with the novelmeasurement procedure described above, provide significantly betterperformance in physically realistic (noisy) situations. Analysis hasshown that this improvement in performance is due both to sensitivityamplitude enhancements (due to alignment of the electric fieldstimulating and recording electric field vectors) and a betterrepresentation (more suitable for reconstruction) of the set ofmeasurements possible by the proposed recording configuration.

A potential problem associated with compound electrodes is thepossibility of a partial electrical short circuit between thestimulating and measuring electrode, due to the close proximity of theseelectrodes. Simulations have indicated that satisfaction will beobtained with spacing of the component electrodes of a compoundelectrode such as to render the voltage associated with this extra(surface) current path approximately 0.1% of that associated with theconventional path (through the region of interest). For a human bodythis requirement translates into a resistance of (for skin surfacealone) approximately 5 MΩ. An example of a suitable compound electrodeis shown in FIGS. 8 and 9. The compound electrode comprises an annularouter electrode 46 surrounding a circular inner electrode 48 with anannular slot 50 between them. The electrodes 46 and 48 are bonded to aninsulating planar support 52 and their exposed surfaces are coated withlayers of conductive gel 54 and 56, respectively. An “O” ring 58 ofinsulating material is located in the annular slot 50. The diameter ofthe “O” ring 58 is approximately equal to the depth of the annular slot50 so that, when the compound electrode is applied to the surface of thevolume under investigation, the “O” ring 58 will prevent gel 54/56 fromexuding across the annular slot 50 and causing, effectively, ashort-circuit between the inner and outer electrodes. In use, aplurality of such compound electrodes would be distributed about thesurface of the body being investigated. Current could be applied to therespective outer electrodes of a pair of compound electrodes and thepotential difference recorded between the inner electrodes of the samepair. Conversely, the inner electrodes could be stimulated and thepotential difference recorded between the outer electrodes.

It should be appreciated that other configurations of compound electrodecould be used. For example, either or both of the electrodes could berectangular. It is also envisaged that each compound electrode mightcomprise an array or grid of stimulation electrodes interspersed with anarray or grid of recording electrodes.

The annular electrode array of FIGS. 2 and 3, whether with theindividual electrodes or with the compound electrodes, is well suitedfor medical diagnostics applications applied to a patient's head, limbor torso. Nevertheless, the enhanced sensitivity approach illustratedwith the annular geometry can also be applied to other electrodeconfigurations. Thus, FIG. 10 illustrates a two-dimensional array ofelectrode cells which is shown as rectangular but could have othershapes. This electrode array is envisaged for ground imagingapplications, such as landmine detection. The array comprises juxtaposedindividual electrode cell units 60. As shown in FIG. 11, each cellcomprises a pair of electrodes R, S immersed in a conductive material,for example a jelly formed from agar and saline solution, as before.

The cell units 60 lie on a bed 62 (FIG. 10) of conductive material thatprovides the electrical interface with the ground. This bed 62 wouldhave insulating partitions (not shown) to maintain anisotropicconductivity.

FIG. 12 illustrates another possible embodiment, where a flexible vest64 comprises similar individual electrode cells 66 forming a cylindricalarray which, as shown, can be wrapped around a human torso and used forthree-dimensional imaging. It will be appreciated that other geometriesare also feasible, such as a special cap for head imaging applicationsor a special brassiere for breast imaging applications.

It should be appreciated that, if the radially-spaced electrodes S/R ofFIGS. 2-4 and 10-12 were replaced by compound electrodes, theagar-filled compartments or cells would not be required, since thecompound electrodes could lie flat upon the surface. However, it isenvisaged that, to facilitate calculations, the compound electrodeswould still be in a rigid support, if necessary, with an interveningsponge 36, or the like.

Reconstruction Technique

The proposed reconstruction technique is based on the construction of aprobabilistically regulated, pseudo inverse of the sensitivity matrixintroduced above and mentioned in step 7.4. The construction of thispseudo inverse is very straightforward, and follows the following steps:

Calculate the singular value decomposition of the sensitivity matrix.

S=UΛV^(T)  (5)

Replace each singular value λ_(i) in Λ=diag(λ_(i)) with λ_(i)^(#)=λ_(i)/(λ_(i) ²+μ²), producing Λ^(#)=diag(λ_(i) ^(#)). The parameterμ is the ratio of the noise in the measured potential differences to theroot mean square (RMS) of the conductivity distribution. Thus, in thissense it is the inverse of the SNR.

Form the pseudo inverse

S^(#)=VΛ^(#)U^(T)  (6)

which can be used to compute conductivity perturbations from potentialdifference recordings, i.e. reconstruct the EIT image, since$\begin{matrix}{{{\Delta \quad \sigma_{i}} = {\sum\limits_{j = 1}^{n}\quad {S_{ij}^{\#}\Delta \quad Z_{j}}}},} & (7)\end{matrix}$

where n is the number of independent measurements taken,

This approach has been found to respect the inherent low pass filteringof the EIT process, and offers a rapid and robust option for EIT imagereconstruction.

FIGS. 13A to 13I illustrate a comparison between the novel measurementprocedure set out in Table 1, using compound electrodes as per FIG. 8,and the measurement procedure disclosed by Brown at al. in U.S. Pat. No.4,617,939, but in both cases using the reconstruction techniquedescribed above. FIGS. 13A to 13I depict the reconstruction of aperturbation covering approximately 10% of the diameter of a circularregion of interest at three different locations. As shown in FIGS. 13A,13D and 13G, with zero noise, both Brown et al.'s procedure and theprocedure of the present invention reproduce the perturbation veryaccurately. Thus, FIG. 13A shows a maximum a posteriori (MAP) estimateof a perturbation near the circumference of the region. FIG. 13B showsthe (MAP) estimate of the differential conductivity distribution Δσ fora circular array of 16 compound electrodes of the kind shown in FIG. 8.FIG. 13C shows the corresponding MAP estimate for the conventionalelectrode configuration fo FIG. 1 using Brown et al.'s measurementtechnique.

FIGS. 13D to 13F correspond to FIGS. 13A to 13C fo a perturbation whichis closer to the middle of the rigion and FIGS. 13G to 13I are thecorresponding reconstructions for a perturbation at the centre of theregion.

The present invention embraces various modification and substitutions.For example, the electrodes could be in a fixed array and a separatecurrent generator provided for cach pair stimulated. Alternatively, asingle current generator could be used to stimulate cach pair ofelectrodes in turn, using a commutation switching circuit, enabling amore expensive current generator to be used.

It is also envisaged that only two stimulating electrodes and tworecording electrodes could be used. The various locations would brpredefined and the electrodes repositioned at selected locations in turnuntil all lacations had been stimulated as required.

It is envisaged that, instead of providing a personal computer with aDSP card for performing the reconstruction, a suitable custom integratedcircuit, preprogrammed with the reconstruction algorithm software, couldbe combined with the electronic conditioning circuitry in an interfacewhich would connect to a conventional personal computer and/or evendirectly to a display device.

INDUSTRIAL APPLICABILITY

The compound electrode arrangement may be easier to manufacture. Themeasurement procedure facilitates simpler implementations for a givensensitivity.

What is claimed is:
 1. A method of determining electrical impedancetomography of a conductive volume (12) comprising the steps ofselecting, in turn, each of a plurality of pairs of locations (S) upon asurface of the volume (12) and supplying a stimulation current to thesurface by way of the selected pair of locations, and recording, foreach selected pair, a resulting potential difference between at leastone pair (R) of the remaining locations, and processing the recordedpotential differences to plot electrical conductivity distributionwithin said volume, and, for a particular pair of locations stimulated,selecting from among the remaining locations, for recordal, the pair orpairs of locations which, if stimulated, would produce an electric fieldwith vectors most closely aligned with the corresponding vectors of theelectric field produced by stimulation of said particular pair oflocations, and recording said potential difference at the said pair orpairs of locations so selected for recordal.
 2. A method of determiningelectrical impedance tomography according to claim 1, using a pluralityof electrodes (S₁-S₁₆, R₁-R₁₆) disposed upon or adjacent said surfaceeach at a respective one of said plurality of locations, comprising thesteps of; (i) applying a stimulation current to said volume by way of afirst (S₁) and a second (S₂) of said plurality of electrodes atcorresponding first and second locations; (ii) simultaneously recordingthe resulting potential difference between that pair (R₁, R₂) of theremaining electrodes at said pair of locations which, if stimulated,would produce electric field vectors most closely aligned with theelectric field vectors produced by stimulation of said particular pairof locations; (iii) applying a stimulation current to said body by wayof two electrodes (S₂, S₃) at least one of which was not stimulated in aprevious step; (iv) simultaneously recording the resulting potentialdifference between that pair (R₂, R₃) of the remaining electrodes atsaid locations which, if stimulated, would produce an electric fieldwith vectors most closely aligned with the corresponding vectors of theelectric field produced by the stimulation current applied in step(iii).
 3. A method according to claim 2, wherein stimulation current isapplied to a said first and second of said plurality of electrodes withno intervening electrodes.
 4. A method according to claim 2, whereinsaid stimulation current is applied to a said first and second of saidplurality of electrodes that are spaced apart with one or more otherelectrodes therebetween.
 5. A method according to claim 4, wherein eachperformance of steps (iii) and (iv) applies said stimulation current toa pair of electrodes that are spaced apart with a different number ofintervening electrodes therebetween.
 6. A method according to claim 2,wherein, in said steps (i) and (ii), said stimulation current is appliedto a said first and second of said electrodes that have no electrodestherebetween, and said potential difference recorded, and, in said steps(iii) and (iv), a stimulation current is applied to a said twoelectrodes that have one or more electrodes therebetween, and theresulting potential difference recorded.
 7. A method according to claim2, wherein the stimulating currents are applied to selected pairs of afirst group (S₁-S₁₆) of the plurality of electrodes and the resultingpotential differences are recorded at selected pairs of a second group(R₁-R₁₆) of the plurality of electrodes, the electrodes (R₁-R₁₆) of oneof the groups are closer to the surface than the electrodes (S₁-S₁₆) ofthe other of the groups.
 8. A method according to claim 7, wherein eachelectrode of the first group is substantially aligned with acorresponding electrode of the second group in a direction extendingsubstantially normal to said surface and said potential difference isrecorded between that pair of said electrodes which are aligned with thepair of electrodes to which the stimulation current is applied.
 9. Amethod according to claim 2, wherein each electrode means comprises astimulation electrode (46) and a recording electrode (48) closelylocated to each other and both the same distance from said surface, thestep of applying stimulation current applies the stimulation current tothe stimulation electrodes (46) of two electrode means, respectively,and the corresponding potential difference is measured between therecording electrodes (48) of the same two electrode means.
 10. A methodaccording to claim 9, wherein one of the stimulating electrode (46) andthe recording electrode (48) surrounds the other.
 11. An electrodearrangement for an electrical impedance tomography system comprising afirst group of electrodes (R₁-R₁₆) and a second group of electrodes(S₁-S₁₆) and support means (24,26,28,30) for supporting the electrodesadjacent a surface of a volume (12′) the electrical impedance of whichis to be mapped by the system, wherein the first group of electrodes(R₁-R₁₆) is closer than the second group of electrodes (S₁-S₁₆) to apart of the support means which, in use, will be adjacent said surface.12. An electrode arrangement according to claim 11, each electrode ofthe first group (R₁-R₁₆) is substantially aligned with an adjacentelectrode of the second group (S₁-S₁₆) in a direction extendingsubstantially normal, in use, to said surface.
 13. An electrodearrangement according to claim 12, wherein the support means(24,26,28,30) comprises an annular structure, the first group ofelectrodes (R₁-R₁₆) and the second group of electrodes (S₁-S₁₆) beingarranged in an inner ring and an outer ring, respectively, about acentral part of the annular structure.
 14. An electrode arrangementaccording to claim 13, wherein the annular structure (24,26,28,30) iscircular and the spacing between the inner ring of electrodes and theouter ring of electrodes is about one quarter of the diameter of theinner ring.
 15. An electrode arrangement according to claim 11, whereinthe support means (24,26,28,30) comprises an annular structure, thefirst group of electrodes (R₁-R₁₆) and the second group of electrodes(S₁-S₁₆) being arranged in an inner ring and an outer ring,respectively, about a central part of the annular structure.
 16. Anelectrode arrangement according to claim 15, the annular structure(24,26,28,30) is circular and the spacing between the inner ring ofelectrodes and the outer ring of electrodes is about one quarter of thediameter of the inner ring.
 17. An electrode arrangement according toclaim 11, wherein the support means comprises a plurality ofcompartments (32 ₁-32 ₁₆), each comprising a conductive medium forcontacting the surface of a volume (12′) to be imaged, and lowerconductivity partitions (28 ₁-28 ₁₆) between adjacent compartments, eachcompartment housing a pair of electrodes comprising one electrode fromsaid first group (S₁-S₁₆) and one electrode from said second group(R₁-R₁₆).
 18. An electrode arrangement according to claim 17, whereinthe electrodes are supported in a planar array (60,62), and eachelectrode of said first group is spaced from an associated electrode ofsaid second group in a direction substantially perpendicular to theplane of the array.
 19. An electrode arrangement according to claim 11,wherein the support means (24,26,28,30) is rigid and a conductiveinterface medium (36) is disposed for juxtaposing between an innersurface of said support means and the surface of the volume (12) to bemeasured, the interface medium comprising a material that is conformableto contour variations of said surface of the volume.
 20. An electrodearrangement according to claim 19, wherein the interface medium material(36) has a conductivity comparable to that of the volume to be measured.21. An electrode arrangement according to claim 19, wherein eachelectrode of the first group (R₁-R₁₆) is substantially aligned with anadjacent electrode of the second group (S₁-S₁₆) in a direction extendingsubstantially normal, in use, to said surface.
 22. An electrodearrangement according to claim 19, wherein the support means(24,26,28,30) comprises an annular structure, the first group ofelectrodes (R₁-R₁₆) and the second group of electrodes (S₁-S₁₆) beingarranged in an inner ring and an outer ring, respectively, about acentral part of the annular structure.
 23. An electrode arrangementaccording to claim 22, wherein the annular structure (24,26,28,30) iscircular and the spacing between the inner ring of electrodes and theouter ring of electrodes is about one quarter of the diameter of theinner ring.
 24. An electrode arrangement according to claim 19, whereinthe support means comprises a plurality of compartments (32 ₁-32 ₁₆),each comprising a conductive medium for contacting the surface of avolume (12′) to be imaged, and lower conductivity partitions (28 ₁-28₁₆) between adjacent compartments, each compartment housing a pair ofelectrodes comprising one electrode from said first group (S₁-S₁₆) andone electrode from said second group (R₁-R₁₆).
 25. An electrodearrangement according to claim 24, wherein the interface medium material(36) has a conductivity comparable to that of the volume to be measured.26. An electrode arrangement according to claim 19, wherein theelectrodes are supported in a planar array (60,62), and each electrodeof said first group is spaced from an associated electrode of saidsecond group in a direction substantially perpendicular to the plane ofthe array.
 27. An electrode arrangement according to claim 11, whereinthe support means (24,26,28,30) has anisotropic conductivity with itsconductivity in said direction normal to said surface, in use, beingsignificantly higher than its conductivity in directions transversethereto.
 28. An electrode arrangement according to claim 27, wherein thesupport means (24,26,28,30) comprises a plurality of higher conductivitysectors (32) alternating with, and defined by, a plurality of lowerconductivity regions (28).
 29. An electrode arrangement according toclaim 27, wherein each electrode of the first group (R₁-R₁₆) issubstantially aligned with an adjacent electrode of the second group(S₁-S₁₆) in a direction extending substantially normal, in use, to saidsurface.
 30. An electrode arrangement according to claim 27, wherein thesupport means (24,26,28,30) comprises an annular structure, the firstgroup of electrodes (R₁-R₁₆) and the second group of electrodes (S₁-S₁₆)being arranged in an inner ring and an outer ring, respectively, about acentral part of the annular structure.
 31. An electrode arrangementaccording to claim 30, wherein the annular structure (24,26,28,30) iscircular and the spacing between the inner ring of electrodes and theouter ring of electrodes is about one quarter of the diameter of theinner ring.
 32. An electrode arrangement according to claim 27, whereinthe support means comprises a plurality of compartments (32 ₁-32 ₁₆),each comprising a conductive medium for contacting the surface of avolume (12′) to be imaged, and lower conductivity partitions (28 ₁-28₁₆) between adjacent compartments, each compartment housing a pair ofelectrodes comprising one electrode from said first group (S₁-S₁₆) andone electrode from said second group (R₁-R₁₆).
 33. An electrodearrangement according to claim 27, wherein the electrodes are supportedin a planar array (60,62), and each electrode of said first group isspaced from an associated electrode of said second group in a directionsubstantially perpendicular to the plane of the array.
 34. An electrodearrangement according to claim 27, wherein the support means(24,26,28,30) is rigid and a conductive interface medium (36) isdisposed for juxtaposing between an inner surface of said support meansand the surface of the volume (12) to be measured, the interface mediumcomprising a material that is conformable to contour variations of saidsurface of the volume.
 35. An electrode arrangement according to claim34, wherein the interface medium material (36) has a conductivitycomparable to that of the volume to be measured.
 36. An electrodearrangement for an electrical impedance tomography system comprising aplurality of electrodes (S₁-S₁₆, R₁-R₁₆) in an array mounted in asupport (24,26,28,30) for supporting the electrodes adjacent a surfaceof a volume (12′) to be imaged, wherein the support comprises aplurality of low conductivity sections (28 ₁-28 ₁₆) alternating with aplurality of high conductivity sections (32 ₁-32 ₁₆) so that itsconductivity in a direction that, in use, is normal to the surface issignificantly greater than its conductivity in a transverse direction,and the electrodes (R₁-R₁₆, S₁-S₁₆) are disposed in the highconductivity sections (32 ₁-32 ₁₆), respectively, so as to be spaced, inuse, from said surface.
 37. An electrode arrangement according to claim36, wherein the support comprises a plurality of compartments (32 ₁-32₁₆), each separated from neighbouring compartments by an insulatingpartition (28 ₁-28 ₁₆), each compartment comprising a material having aconductivity comparable to the conductivity of the volume theconductivity distribution of which is to be measured and containing atleast one of the electrodes.
 38. An electrode arrangement for anelectrical impedance tomography system comprising an array of electrodes(S₁-S₁₆, R₁-R₁₆) fixed spatially relative to each other in a rigidsupport (24,26,28,30), and an interface medium (36) for interfacing therigid support to a surface of a volume (12′) the conductivitydistribution of which is to be measured, the interface medium beingconductive so as to connect the electrodes electrically to the surfaceand pliable so as to conform to variations in relief of the surface. 39.An electrode arrangement according to claim 38, wherein the interfacemedium material (36) has a conductivity comparable to that of the volumeto be measured.
 40. An electrical impedance tomograph according to claim39, wherein the support means comprises a plurality of compartments (32₁-32 ₁₆), each comprising a conductive medium for contacting the surfaceof a volume (12′) to be imaged, and lower conductivity partitions (28₁-28 ₁₆) between adjacent compartments, each compartment housing a pairof electrodes comprising one electrode from said first group (S₁-S₁₆)and one electrode from said second group (R₁-R₁₆).
 41. An electricalimpedance tomograph comprising a first group of electrodes (R_(1-R) ₁₆)and a second group of electrodes (S₁-S₁₆) and support means(24,26,28,30) for supporting the electrodes adjacent a surface of avolume (12′) the electrical impedance of which is to be mapped by thesystem, wherein the first group of electrodes (R₁-R₁₆) is closer thanthe second group of electrodes (S₁-S₁₆) to a part of the support meanswhich, in use, will be adjacent said surface, and further comprisingmeans (16,18,20) for stimulating, sequentially, pairs of electrodes(S₁-S₁₆) and, for each pair stimulated, measuring correspondingpotential differences between a pair or pairs of the remainingelectrodes, and processing the measured potentials to map electricalconductivity distribution of a volume (12′).
 42. An electrical impedancetomograph according to claim 41, wherein each electrode of the firstgroup (R₁-R₁₆) is substantially aligned with an adjacent electrode ofthe second group (S₁-S₁₆) in a direction extending substantially normal,in use, to said surface.
 43. An electrical impedance tomograph accordingto claim 42, wherein the support means (24,26,28,30) comprises anannular structure, the first group of electrodes (R₁-R₁₆) and the secondgroup of electrodes (S₁-S₁₆) being arranged in an inner ring and anouter ring, respectively, about a central part of the annular structure.44. An electrical impedance tomograph according to claim 43, wherein theannular structure (24,26,28,30) is circular and the spacing between theinner ring of electrodes and the outer ring of electrodes is about onequarter of the diameter of the inner ring.
 45. An electrical impedancetomograph according to claim 41, wherein the support means (24,26,28,30)comprises an annular structure, the first group of electrodes (R₁-R₁₆)and the second group of electrodes (S₁-S₁₆) being arranged in an innerring and an outer ring, respectively, about a central part of theannular structure.
 46. An electrical impedance tomograph according toclaim 41, wherein the electrodes are supported in a planar array(60,62), and each electrode of said first group is spaced from anassociated electrode of said second group in a direction substantiallyperpendicular to the plane of the array.
 47. An electrical impedancetomograph according to claim 41, wherein the support means (24,26,28,30)is rigid and a conductive interface medium (36) is disposed forjuxtaposing between an inner surface of said support means and thesurface of the volume (12) to be measured, the interface mediumcomprising a material that is conformable to contour variations of saidsurface of the volume.
 48. An electrical impedance tomograph accordingto claim 47, wherein the interface medium material (36) has aconductivity comparable to that of the volume to be measured.
 49. Anelectrical impedance tomograph according to claim 41, wherein thesupport means (24,26,28,30) has anisotropic conductivity with itsconductivity in said direction normal to said surface, in use, beingsignificantly higher than its conductivity in directions transversethereto.
 50. An electrode impedance tomograph according to claim 49,wherein the support means (24,26,28,30) comprises a plurality of higherconductivity sectors (32) alternating with, and defined by, a pluralityof lower conductivity regions (28).
 51. An electrical impedancetomograph according to claim 41, wherein the support comprises aplurality of low conductivity sections (28 ₁-28 ₁₆) alternating with aplurality of high conductivity sections (32 ₁-32 ₁₆) so that itsconductivity in a direction that, in use, is normal to the surface issignificantly greater than its conductivity in a transverse direction,and the electrodes (R₁-R₁₆, S₁-S₁₆) are disposed in the highconductivity sections (32 ₁-32 ₁₆), respectively, so as to be spaced, inuse, from said surface.
 52. An electrical impedance tomograph accordingto claim 51, wherein the support comprises a plurality of compartments(32 ₁-32 ₁₆), each separated from neighbouring compartments by aninsulating partition (28 ₁-28 ₁₆), each compartment comprising amaterial having a conductivity comparable to the conductivity of thevolume the conductivity distribution of which is to be measured andcontaining at least one of the electrodes.
 53. An electrical impedancetomograph for use in a method of determining electrical impedancetomography of a conductive volume (12) by selecting, in turn, each of aplurality of pairs of locations (S) upon a surface of the volume (12)and supplying a stimulation current to the surface by way of theselected pair of locations, and recording, for each selected pair, aresulting potential difference between at least one pair (R) of theremaining locations, and processing the recorded potential differencesto plot electrical conductivity distribution within said volumecomprising: (i) a plurality of electrodes (S₁-S₁₆, R₁-R₁₆) for disposingupon or adjacent said surface, each at a respective one of saidplurality of locations; (ii) means (16) for selecting each pair(S₁,S₂;S₂,S₃, . . . S₁₅,S₁₆) of electrodes in turn and applying astimulation current thereto and, for each particular pair of locationsstimulated, the pair or pairs of locations which, if stimulated, wouldproduce an electric field with vectors most closely aligned with thecorresponding vectors of the electric field produced by stimulation ofsaid particular pair of locations; and recording the potentialdifference between each pair of electrodes selected for recordal; and(iii) means (18) for processing the recorded potential differences todetermine the electrical impedance tomography for the volume.